R中的线性回归模型矩阵

Question

Considering the model , where

And the matrix of $X$ is

How do I input this matrix into R?

Answer 1

Assuming that x = 1,2, ... , N, N=10 and y = 2x + ε, ε ~ N(0,1) then you would write something like this:

N = 10;
set.seed(123)
x =  1:N
e = rnorm(N)  
y = 2*x + e;
mod <- lm( y ~x);
Xmatrix = matrix( c(rep(1,N), x), ncol=2)

Please see the following link on Matrices and matrix computations in R for more details on tihs matter.

Answer 2

您可以将该矩阵输入R并执行Y〜X，也可以省略截距并执行Y〜$ {X} _i $ -1，其中$ X_i $只是一个向量。